176 (#238) ############################################ WOOLLEN AND WORSTED SPINNING Botany 2" to 4" 6 or 7 . . thus reasonable to infer that fineness and length of fibre are factors to be taken into consideration. Then if the following lengths are taken as the average for the respective tops, as analysed on the Schlumberger machine : Length Fineness Lustre 7" to 9" 1/500" to 1/800" Cross-bred 4" to 7" 1/800" to 1/1000' 1/1000" to 1/1300" the reason for 5 or 6 operations for lustre and demi-lustre wools ; cross-bred wools; and 7 or 9 botany wools will be apparent. It must be conceded, however, that this is empirical and not scientific, and that a research involving the higher mathematics is here called for, and possibly in the near future will be undertaken. The problem of " draft and doublings "may now be clearly stated. Taking a 256 dram for a 40-yd. (4 oz. for 10 yd.) top and working to a 4-dram roving (which again would be given a draft-without doubling-of 4.5 to obtain 1/30's count), the problem involved may be set out as follows : Top I 2 3 4 5 6 7 8 9 operations Weight in drams. 256 4 Draft Doublings. (5) (5) (5) (4) (4) (3) (3) (2) (2) It will here be noted that if the doublings are given the total draft required may be readily obtained. Thus, if working empirically the doublings given in brackets are adopted, then the total draft will be 64* X5X5X5 X 4 X 4*3*3* 2 X 2 = 45920 and 45920 5.5 equal drafts for the nine operations for a 4 dr. roving. * 256 4 - 64 dominant draft. 176